Chapter 1 - Tools of Geometry

Vocabulary flashcards covering measurement error, geometry basics, angles, 2D and 3D shapes, and transformations based on Chapter 1 notes.

Absolute Error

The actual, physical difference between a measured value and its true, exact value.

Relative Error

The absolute error divided by the true value, often expressed as a percentage to show how significant the error is relative to the size of the object.

Significant Digits

The digits in a decimal number that carry meaning contributing to its precision. This includes all non-zero numbers, zeros between them, and trailing zeros.

Point

A precise location in space that has no size, length, width, or depth.

Line

A straight, one-dimensional path that extends infinitely in both opposite directions.

Linear Segment (Line Segment)

A measurable piece of a line bounded by two distinct endpoints.

Ray

A part of a line that has one starting endpoint and goes on infinitely in the other direction.

Plane

A flat, two-dimensional surface that extends infinitely in all directions.

Collinear

Three or more points that lie on the exact same straight line.

Coplanar

Points, lines, or shapes that lie on the exact same plane.

Intersection

The exact point or set of points where two lines, planes, or figures cross one another.

Distance

The physical length of the shortest path connecting two points.

Midpoint

The exact middle point of a line segment, dividing it into two perfectly equal parts.

Segment Bisector

A line, ray, or segment that passes directly through the midpoint of another line segment, cutting it in half.

Construction

Drawing geometric shapes, angles, or lines with perfect accuracy using only a compass and a straightedge (no rulers or protractors).

Angle

A figure formed by two rays sharing a common endpoint.

Vertex

The common endpoint where two rays meet to form an angle, or where the sides of a shape meet.

Degree

A unit of measurement for angles. A full, complete circle is $360$ degrees.

Acute Angle

An angle measuring greater than $0$ degrees but less than $90$ degrees.

Right Angle

An angle measuring exactly $90$ degrees. Creating $2$ perpendicular lines.

Obtuse Angle

An angle measuring more than $90$ degrees but less than $180$ degrees.

Adjacent Angles

Two angles that share a common side and vertex, but do not overlap (they sit side-by-side).

Complementary Angles

Two angles whose measures add up to exactly $90$ degrees.

Supplementary Angles

Two angles whose measures add up to exactly $180$ degrees.

Linear Pair

A pair of adjacent angles formed by intersecting lines that add up to $180$ degrees, creating a straight line along their unshared sides.

Vertical Angles

A pair of opposite angles made by two intersecting lines. They are completely equal to each other and not necessarily "vertical".

Angle Bisector

A ray or line that divides an angle exactly in half into two smaller, equal angles.

Perpendicular Side (or Lines)

Two lines or sides that intersect to form perfectly square, $90$-degree right angles.

Congruent

Figures, segments, or angles that have the exact same size and shape.

Polygon

A closed, flat figure made entirely of straight line segments.

n-gon

A polygon with "n" number of sides. This term is used when the shape has too many sides for a common name.

Vertex of a Polygon

The corner point where two sides of the polygon meet.

Equilateral Polygon

A polygon where all sides are exactly the same length.

Equiangular Polygon

A polygon where all interior angles are exactly the same measure.

Regular Polygon

A polygon that is perfectly balanced—it is both equilateral (all sides equal) and equiangular (all angles equal).

Convex Polygon

A standard polygon where no interior angles are greater than $180$ degrees. It has no "dents."

Concave Polygon

A polygon that has at least one interior angle greater than $180$ degrees, causing the shape to "cave" inward.

Interior

The inside space contained within a geometric figure.

Exterior

The outside space completely surrounding a geometric figure.

Base

The side or face on which a geometric figure is assumed to rest.

Perimeter

The total continuous distance around the outside border of a 2D shape.

Area

The amount of 2D flat space contained within a figure.

Circumference

The perimeter (the distance around the outside) of a circle.

Polyhedron

A 3D solid figure where all faces are flat polygons (no curved surfaces).

Face

One of the flat polygon surfaces on the outside of a polyhedron.

Edge

The straight line segment where two faces of a solid figure meet.

Prism

A polyhedron with two identical, parallel bases connected by flat rectangular faces.

Pyramid

A polyhedron with a polygon base and triangular sides that all meet at a single top point.

Cone

A 3D figure with a circular base that tapers smoothly to a single point.

Sphere

A perfectly round 3D solid where every point on the surface is the same distance from the center.

Surface Area

The total area of all the exterior faces of a 3D object added together.

Volume

The amount of 3D space an object occupies.

Rigid Transformation

The general term for any operation that alters the position, keeping the sides and angles congruent.

Preimage

The original geometric figure before any transformation has occurred.

Image

The figure after a transformation is complete. Designated with an apostrophe; A'.

Translation

A transformation that slides a figure horizontally, vertically, or both, without spinning or flipping it.

Reflection

A transformation that flips a figure across a line to create a mirror image.

Rotation

A transformation that turns a figure around a fixed central point.